Notation and Geometric Ideas

Identify the type of integral described by the notation.

An integral of the form is a:
An integral of the form is a:
An integral of the form is a:
An integral of the form is a:

Computations

These questions are more open ended but are meant to guide your studying a bit.

What is your thought process when asked to evaluate for some and some ?
What is your thought process when asked to evaluate for some and some ?
What is your thought process when asked to evaluate for some vector field and some ?
How do you check whether a vector field is conservative? How does this relate to the curl?
What does the Fundamental Theorem of Line Integrals say, and what are its main consequences for the purposes of this class?
How can the Fundamental Theorem of Line Integrals and its consequences help you compute vector line integrals?
When can you use the Fundamental Theorem of Line Integrals?
What does Green’s Theorem say? What are its conditions, and in what instances can it be used?
Can we use Green’s Theorem if is conservative? What does it tell us in this case?
Suppose we have a line integral . If we need to close the curve to use Green’s Theorem, what are the steps we must carry out in order to solve the original integral?
When given a vector line integral , what is your thought process in determining what method to use?